This week with in the Marketing Research & Strategy class and the help of “the Market research toolbox” book, we have learned how to determine a sample size, something that we are going to apply to our final project. The book I just mentioned gives us an efficient way to be able to calculate the size of our sample. The process that we need to do in order to find a sample size is divided into 3 steps. The first step is to square the Z value (that we are going to find in the tables showing the area under the curve for normally distributed data) associated with the desired confidence interval. The second step is to multiply the previous number by the population variance. And the last step is to divide by the square of the desired precision.
In page 303 exercise 4, we are presented with 3 different problems that can be solved using these three steps in order to obtain the sample size. Problem d) is about a firm that wants to track satisfaction on a quarterly basis using a 10-point scale. They would like a precision of ±0.05 – that is to be able to interpret a change in average satisfaction from 8.90 to 8.95 as a true increase in customer satisfaction (95 percent confidence). So in order to find the sample size our first step is to use the confidence interval of 95% to find the Z. We know that a confidence interval of 95 has a Z value of 2. Once we have figured out the Z value, we need to square it, which is going to be equal to 4. Our second step is to multiply 4 by the population variance. The population variance is the only number that is not given to us, so in order to find it we need to check the table 13.1 in page 298 (estimated variance for rating scales). We can see that the variance is going to be 3 because we are dealing with a normal distribution. And our last step should be to divide the result of the previous multiplication by the square of the desired precision, which in this case is (0.05)2 = 0.0025.
This is the way it should be:
22 x 3 / 0.0025 = 48000 customers
Even though this precision works for this specific problem, I think it would have been better to go with a higher number so it doesn’t limit study. In the book Edwar McQaurrie suggests that going lower than 5 percentage point is not a smart move. “a desire for high precision combined with use of high variance scale (10 points rather than 4 points) is going to drive sample size and costs considerably higher”. That being said, there is no reason to conduct a market research for such a narrow precision when you can provably conduct something closer to it with a lower cost. More precision doesn’t mean that you are going to get rid of all the uncertainty, it is always going to be there.